Question: Simplify the following expression: $t = \dfrac{4y^2 - 32y - 80}{y + 2} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $4$ , so we can rewrite the expression: $ t =\dfrac{4(y^2 - 8y - 20)}{y + 2} $ Then we factor the remaining polynomial: $y^2 {-8}y {-20} $ ${2} {-10} = {-8}$ ${2} \times {-10} = {-20}$ $ (y + {2}) (y {-10}) $ This gives us a factored expression: $\dfrac{4(y + {2}) (y {-10})}{y + 2}$ We can divide the numerator and denominator by $(y - 2)$ on condition that $y \neq -2$ Therefore $t = 4(y - 10); y \neq -2$